In this section of the manuscript, we will discuss the quantization of system described above using the field-antifield formalism [1]}, [2]} for BFFT system discussed in ref([3]}, [4]}). For this purpose we will introduce a set of antifields \(\varpi ^{\star }_\mu = (x^{\star }_A, \Theta ^{\star }_a, \lambda ^{\star }_a, C^{\star }_a)\)  corresponding to the fields \(\varpi ^\mu = (x^A, \Theta ^a, \lambda ^a, C^a)\) . Here, fields \( x^A, \Theta ^a\)  and \(\lambda ^a\)  are bosonic and have ghost number zero. The ghosts \(C^a\)  are fermionic and have ghost number one. The corresponding anti-fields have opposite grassmanian parity and ghost number given by minus the ghost number of the corresponding field minus one.
Action in terms of fields and antifields is written as
\(S & = & S_0 + \int dt \big [ x^{\star }_A \lbrace  x^A, {\tilde{\Phi }}_a \rbrace  C^a + {\Theta }^{\star }_b \lbrace  \Theta ^b, {\tilde{\Phi }}_a \rbrace  C^a + \lambda ^{\star }_a {\dot{C}}^a \big ]\) 
